Kinetic model selection and the Hill model in geochemistry

B. D. Turner, B. J. Henley, S. B. Sleap, S. W. Sloan

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)


This study introduces the Hill model for modelling sorption kinetics and illustrates its efficacy using formal model selection procedures. Although the coefficient of determination (R2) value can be used to ensure goodness-of-fit of a particular model to a set of data, a measure that incorporates the number of model parameters, such as the Bayesian information criterion, law of iterated logarithm criterion, Akaike information criterion, and the extra sum-of-squares F-test is necessary to undertake reliable model selection. This study undertook a formal model selection procedure based on these criteria, in combination with the coefficient of determination, for a range of candidate kinetics sorption models [the pseudo-second order (PSO), the intra-particle diffusion (IPD), Power, Elovich, and the four and five parameter Hill models]. It was found that the model order that statistically best described the data was Hill 5 > Hill 4 > pseudo-second order > Elovich > Power > IPD as given by the evidence ratios, information criterion weights and Bayes factors. The extra sum-of-squares F-test, only applicable to nested models, confirms the best fit order as Hill 5 > Hill 4 > PSO models. Two new parameters (T and kHill) have also been defined that give the Hill models a mechanistic meaning directly comparable to the well-defined parameters of the pseudo-second-order model, namely, the pseudo-second-order rate constant kpso and the instantaneous sorption coefficient hpso. In the field of geochemistry the use of the four and five parameter Hill models for describing sorption kinetics has been overlooked with many studies favouring the PSO model. It is strongly recommended that the Hill model be considered more widely as a general predictive tool in geochemistry.

Original languageEnglish
Pages (from-to)2545-2558
Number of pages14
JournalInternational Journal of Environmental Science and Technology
Issue number8
Publication statusPublished - 15 Aug 2015
Externally publishedYes


  • Adsorption
  • AIC
  • Hill model
  • Kinetics
  • Model selection
  • Pseudo-second order

Cite this